Coupled CPD-Aided Tensor Train Decomposition for 2D-DOD and 2D-DOA Estimation in Bistatic MIMO Radar

Conventional CANDECOMP/PARAFAC decomposition (CPD) and Tucker decomposition (TD) have been extensively used in bistatic multiple-input multiple-output (MIMO) radars for angle estimation. However, their specific decomposition methods can cause the loss of crucial information within a high-dimensional tensor, which requires improvements in estimation accuracy. To address this limitation, this study proposes an algorithm based on tensor train decomposition (TTD) to jointly estimate the two-dimensional direction-of-departure (2D-DOD) and two-dimensional direction-of-arrival (2D-DOA) values in bistatic MIMO radars with a uniform planar array geometry. First, a self-correlation tensor model is developed and reshaped into a low-rank four-dimensional (4D) coarray tensor with Vandermonde factors. Then, the tensor-train singular value decomposition (TT-SVD) method is employed to decompose this 4D coarray tensor into a head matrix, a tail matrix, and two third-order TT-core tensors. Furthermore, to mitigate the propagation of estimation errors across different Vandermonde factor matrices, this study designs an innovative coupled CPD model by integrating all inverse lateral slices of the second third-order TT-core tensor. In addition, the iterative least squares algorithm is employed to realize the coupled CPD, yielding three change-of-basis matrices and two Vandermonde factor matrices with trivial ambiguities. Finally, accurate automatic coupling of the 2D-DOD and 2D-DOA estimations is achieved, confirming that the estimated Vandermonde factor matrices have identical column permutations. The simulation results demonstrate that the estimation accuracy of the proposed algorithm is higher than that of the existing tensor decomposition algorithms.